I have problem which I, at least, can't solve analytically. I have a known, complex 2-by-2-by-M matrix A, and a known 2-by-2-by-M matrix T, both symmetric, and want to find a complex 2-by-2-by-M matrix W such that A = W*T*W^T, or equivalently, minimize the residual r = A-W*T*W^T.

I see I forgot to mention some part of the problem. The A and T matrices are measured S-parameters of some connections. The A matrix represents the cascaded connection of two devices, separated by the connection T. Since S-parameters can't be cascaded, I transform them to ABCD parameters, which can be multiplied by each other, hence A = WTW^T.

The residual I get when using fsolve is small when comparing the ABCD parameters (r = A-x*T*X.'), however, the residual of the S-parameters of W is quite bad.

For now I have only used a set of simulated S-parameters for both A, T and W, so I can check how close the estimate actually can get. Since the estimate for the simulated parameters is so bad, I can't use this for the measured data. But as mentioned, I assume I do something wrong in MATLAB, and hope someone can point something out for me. :)

"dm" wrote in message <ig43us$83q$1@fred.mathworks.com>...
> I have problem which I, at least, can't solve analytically. I have a known, complex 2-by-2-by-M matrix A, and a known 2-by-2-by-M matrix T, both symmetric, and want to find a complex 2-by-2-by-M matrix W such that A = W*T*W^T, or equivalently, minimize the residual r = A-W*T*W^T.
>

I'm interested. How do you define symmetry for a 2x2xM matrix,
at least where M will be greater than 1? (I can handle the case
for M == 1.)

I'm also interested in how you plan on doing the required matrix
multiplies. Your function simply writes it as a standard multiply
using * , but that won't work quite as well for general M, at least
in my version of MATLAB.

"John D'Errico" <woodchips@rochester.rr.com> wrote in message <ig4asl$3qt$1@fred.mathworks.com>...
> "dm" wrote in message <ig43us$83q$1@fred.mathworks.com>...
> > I have problem which I, at least, can't solve analytically. I have a known, complex 2-by-2-by-M matrix A, and a known 2-by-2-by-M matrix T, both symmetric, and want to find a complex 2-by-2-by-M matrix W such that A = W*T*W^T, or equivalently, minimize the residual r = A-W*T*W^T.
> >
>
> I'm interested. How do you define symmetry for a 2x2xM matrix,
> at least where M will be greater than 1? (I can handle the case
> for M == 1.)
>
> I'm also interested in how you plan on doing the required matrix
> multiplies. Your function simply writes it as a standard multiply
> using * , but that won't work quite as well for general M, at least
> in my version of MATLAB.
>
> John

What I meant by symmetric is that for every m in [1,M], each 2-by-2 matrix A(:,:,m) is equal to A(:,:,m).' (and the same for each 2-by-2 matrix T(:,:,m)).

I also thought of doing the required operations within a loop, so I have something like

What is a watch list?

You can think of your watch list as threads that you have bookmarked.

You can add tags, authors, threads, and even search results to your watch list. This way you can easily keep track of topics that you're interested in. To view your watch list, click on the "My Newsreader" link.

To add items to your watch list, click the "add to watch list" link at the bottom of any page.

How do I add an item to my watch list?

Search

To add search criteria to your watch list, search for the desired term in the search box. Click on the "Add this search to my watch list" link on the search results page.

You can also add a tag to your watch list by searching for the tag with the directive "tag:tag_name" where tag_name is the name of the tag you would like to watch.

Author

To add an author to your watch list, go to the author's profile page and click on the "Add this author to my watch list" link at the top of the page. You can also add an author to your watch list by going to a thread that the author has posted to and clicking on the "Add this author to my watch list" link. You will be notified whenever the author makes a post.

Thread

To add a thread to your watch list, go to the thread page and click the "Add this thread to my watch list" link at the top of the page.

About Newsgroups, Newsreaders, and MATLAB Central

What are newsgroups?

The newsgroups are a worldwide forum that is open to everyone. Newsgroups are used to discuss a huge range of topics, make announcements, and trade files.

Discussions are threaded, or grouped in a way that allows you to read a posted message and all of its replies in chronological order. This makes it easy to follow the thread of the conversation, and to see what’s already been said before you post your own reply or make a new posting.

Newsgroup content is distributed by servers hosted by various organizations on the Internet. Messages are exchanged and managed using open-standard protocols. No single entity “owns” the newsgroups.

There are thousands of newsgroups, each addressing a single topic or area of interest. The MATLAB Central Newsreader posts and displays messages in the comp.soft-sys.matlab newsgroup.

How do I read or post to the newsgroups?

MATLAB Central

You can use the integrated newsreader at the MATLAB Central website to read and post messages in this newsgroup. MATLAB Central is hosted by MathWorks.

Messages posted through the MATLAB Central Newsreader are seen by everyone using the newsgroups, regardless of how they access the newsgroups. There are several advantages to using MATLAB Central.

Use the Email Address of Your Choice
The MATLAB Central Newsreader allows you to define an alternative email address as your posting address, avoiding clutter in your primary mailbox and reducing spam.

Spam Control
Most newsgroup spam is filtered out by the MATLAB Central Newsreader.

Tagging
Messages can be tagged with a relevant label by any signed-in user. Tags can be used as keywords to find particular files of interest, or as a way to categorize your bookmarked postings. You may choose to allow others to view your tags, and you can view or search others’ tags as well as those of the community at large. Tagging provides a way to see both the big trends and the smaller, more obscure ideas and applications.

Watch lists
Setting up watch lists allows you to be notified of updates made to postings selected by author, thread, or any search variable. Your watch list notifications can be sent by email (daily digest or immediate), displayed in My Newsreader, or sent via RSS feed.

Other ways to access the newsgroups

Use a newsreader through your school, employer, or internet service provider

Pay for newsgroup access from a commercial provider

Use Google Groups

Mathforum.org provides a newsreader with access to the comp.soft sys.matlab newsgroup